Suppose t T T T3, where t is the current time, and A...

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Suppose t ≤ T₁ ≤ T₂ ≤ T3, where t is the current time, and A > 0. Recall that Z(T1, T₂) is the price at time T₁ of a ZCB with maturity T₂ and F(T1, T2, T3) is the forward price at time T₁ for a forward contract with maturity T₂ on a ZCB with maturity T3. a) For each of the pairs of A and B in the table, choose the most appropriate relationship out of >, <, , ?, where ? means the relationship is indeterminate. Give brief reasoning. 2, ≤,=, ? (i) (ii) (iii) (iv) (v) (vi) (vii) A Z(t, T₁) Z(T₁, T₁) Z(t, T₂) Z(T1, T₂) Z(T1, T3) B 1 1 Z(t, T3) Z(T1, T3) Z(T2, T3) Z(T2, T₂+A) F(t, T1, T3) F(t, T2, T3) 0 Z(T₁, T₁+ A) F(t, T₁, T₂) (viii) F(t, T1, T3) (ix) limT→∞ Z(t. T) Remember that at current time t, F(t,...) is known but Z(T,-) is a random variable. b) What can you say about interest rates between T₁ and T₂ if i) Z(t, T₁) Z(t, T₂)? ii) Z(t, T₁) > 0 and Z(t, T₂) = 0? Suppose t ≤ T₁ ≤ T₂ ≤ T3, where t is the current time, and A > 0. Recall that Z(T1, T₂) is the price at time T₁ of a ZCB with maturity T₂ and F(T1, T2, T3) is the forward price at time T₁ for a forward contract with maturity T₂ on a ZCB with maturity T3. a) For each of the pairs of A and B in the table, choose the most appropriate relationship out of >, <, , ?, where ? means the relationship is indeterminate. Give brief reasoning. 2, ≤,=, ? (i) (ii) (iii) (iv) (v) (vi) (vii) A Z(t, T₁) Z(T₁, T₁) Z(t, T₂) Z(T1, T₂) Z(T1, T3) B 1 1 Z(t, T3) Z(T1, T3) Z(T2, T3) Z(T2, T₂+A) F(t, T1, T3) F(t, T2, T3) 0 Z(T₁, T₁+ A) F(t, T₁, T₂) (viii) F(t, T1, T3) (ix) limT→∞ Z(t. T) Remember that at current time t, F(t,...) is known but Z(T,-) is a random variable. b) What can you say about interest rates between T₁ and T₂ if i) Z(t, T₁) Z(t, T₂)? ii) Z(t, T₁) > 0 and Z(t, T₂) = 0?

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Part a Lets assume a continuous compoundde discount rate of r for the purpose of illustration Please ... View the full answer